Problem: Solve for $x$ and $y$ using elimination. ${x-6y = -28}$ ${4x+5y = 62}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ ${-4x+24y = 112}$ $4x+5y = 62$ Add the top and bottom equations together. $29y = 174$ $\dfrac{29y}{{29}} = \dfrac{174}{{29}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-6y = -28}\thinspace$ to find $x$ ${x - 6}{(6)}{= -28}$ $x-36 = -28$ $x-36{+36} = -28{+36}$ ${x = 8}$ You can also plug ${y = 6}$ into $\thinspace {4x+5y = 62}\thinspace$ and get the same answer for $x$ : ${4x + 5}{(6)}{= 62}$ ${x = 8}$